The secondary structure of multiple interacting strands is defined by a list of base pairs (Dirks et al., 2007). A polymer graph for a secondary structure can be constructed by ordering the strands around a circle, drawing the backbones in succession from 5’ to 3’ around the circumference with a nick between each strand, and drawing straight lines connecting paired bases. A secondary structure is pseudoknotted if every strand ordering corresponds to a polymer graph with crossing lines. A secondary structure is connected if no subset of the strands is free of the others. Algorithms are formulated in terms of ordered complexes (Zadeh et al., 2011; Dirks et al., 2007), each corresponding to the structural ensemble of all connected polymer graphs with no crossing lines for a particular ordering of a set of strands. The free energy of an unpseudoknotted secondary structure is calculated using nearest-neighbor empirical parameters for RNA in 1M Na+ (Serra and Turner, 1995; Mathews et al., 1999) or DNA in user-specified Na+ and Mg++ concentrations (SantaLucia, 1998; SantaLucia and Hicks, 2004; Koehler and Peyret, 2005); additional parameters are employed for the analysis of RNA pseudoknots (Dirks and Pierce, 2003).
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- J.N. Zadeh, B.R. Wolfe, N.A. Pierce. Nucleic acid sequence design via efficient ensemble defect optimization. J Comput Chem, 32:439-452, 2011.